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Properties (nonexistence) of conference circulant matrices
by
Veselin Vavrek
Institute of Mathematics, Bulgarian Academy of Sciences, P.O.Box 323, 5000 V. Tarnovo, Bulgaria,
A Hadamard matrix is called cyclic, iff it is written in standard form (first column and row contain only ones) and removing first row and column we obtain a circulant matrix. Is it possible to have Hadamard matrix which is circulant matrix? In this work we consider similar question, but concerning Conference matrices (it is the same as Hadamard, but the main diagonal is all zeroes). Other reason of this paper is connected with [1]. In [1] it is proved that Paley type Conference matrices are equivalent to circulant or negacirculant matrices. Therefore nonexistence of some Conference circulant matrices is essential. In this paper it is shown, that if Conference circulant matrix of order n exists, then the number n-1 is a square. We show also that the matrix must be symmetric.
[1] V. Vavrek, Orderings in a finite field, in preparation.
Date received: August 25, 2003
Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # camb-63.